${{\mathit K}^{\pm}}$ $\rightarrow$ ${{\mathit \ell}^{\pm}}{{\mathit \nu}}{{\mathit \gamma}}$ FORM FACTORS

For definitions of the axial-vector $\mathit F_{\mathit A}$ and vector $\mathit F_{\mathit V}$ form factor, see the “Note on ${{\mathit \pi}^{\pm}}$ $\rightarrow$ ${{\mathit \ell}^{\pm}}{{\mathit \nu}}{{\mathit \gamma}}$ and ${{\mathit K}^{\pm}}$ $\rightarrow$ ${{\mathit \ell}^{\pm}}{{\mathit \nu}}{{\mathit \gamma}}$ Form Factors” in the ${{\mathit \pi}^{\pm}}$ section. In the kaon literature, often different definitions $\mathit a_{\mathit K}$ = $\mathit F_{\mathit A}/\mathit m_{\mathit K}$ and $\mathit v_{\mathit K}$ = $\mathit F_{\mathit V}/{\mathit m}_{{{\mathit K}}}$ are used.

$\mathit F_{\mathit A}$ $+$ $\mathit F_{\mathit V}$, SUM OF AXIAL-VECTOR AND VECTOR FORM FACTOR FOR ${{\mathit K}}$ $\rightarrow$ ${{\mathit e}}{{\mathit \nu}_{{{e}}}}{{\mathit \gamma}}$

INSPIRE   JSON  (beta) PDGID:
S010F+E
VALUE EVTS DOCUMENT ID TECN  COMMENT
$\bf{ 0.133 \pm0.008}$ OUR AVERAGE  Error includes scale factor of 1.3.  See the ideogram below.
$0.125$ $\pm0.007$ $\pm0.001$ 1.4k 1
AMBROSINO
2009E
KLOE $\mathit E_{{{\mathit \gamma}}}$ in $10 - 250$ MeV, ${{\mathit p}_{{{e}}}}>$ 200 MeV/c
$0.147$ $\pm0.011$ 51 2
HEINTZE
1979
SPEC
$0.150$ ${}^{+0.018}_{-0.023}$ 56 3
HEARD
1975
SPEC
1  AMBROSINO 2009E measures the absolute value $\vert F_{A}$ + F$_{V}\vert $ which is parametrized as $\vert F_{A}$ + F$_{V}\vert $ = F$_{V}$ (1 + ${{\mathit \lambda}}(1−$x)) + F$_{A}$, x = 2$\mathit E_{{{\mathit \gamma}}}/{\mathit m}_{{{\mathit K}}}$. (F$_{A}$ + F$_{V}$) and ${{\mathit \lambda}}$ are fit parameters. The fitted value of ${{\mathit \lambda}}$ = $0.38$ $\pm0.20$ $\pm0.02$ with a correlation of $-0.93$ between (F$_{A}$ + F$_{V}$) and ${{\mathit \lambda}}$.
2  HEINTZE 1979 quotes absolute value of $\vert \mathit F_{\mathit A}$ $+$ $\mathit F_{\mathit V}\vert $ sin$\theta _{\mathit c}$. We use sin$\theta _{\mathit c}$ = $\mathit V_{\mathit us}$ =$~0.2205$.
3  HEARD 1975 quotes absolute value of $\vert \mathit F_{\mathit A}$ $+$ $\mathit F_{\mathit V}\vert $ sin$\theta _{\mathit c}$. We use sin$\theta _{\mathit c}$ = $\mathit V_{\mathit us}$ =$~0.2205$.

           $\mathit F_{\mathit A}$ $+$ $\mathit F_{\mathit V}$, SUM OF AXIAL-VECTOR AND VECTOR FORM FACTOR FOR ${{\mathit K}}$ $\rightarrow$ ${{\mathit e}}{{\mathit \nu}_{{{e}}}}{{\mathit \gamma}}$
References